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Tidal interactions are important in driving spin and orbital evolution inplanetary and stellar binary systems, but the fluid dynamical mechanismsresponsible remain incompletely understood. One key mechanism is theinteraction between tidal flows and convection. Turbulent convection is thoughtto act as an effective viscosity in damping large-scale tidal flows, but thereis a long-standing controversy over the efficiency of this mechanism when thetidal frequency exceeds the turnover frequency of the dominant convectiveeddies. This high frequency regime is relevant for many applications, such asfor tides in stars hosting hot Jupiters. We explore the interaction betweentidal flows and convection using hydrodynamical simulations within a localCartesian model of a small patch of a convection zone of a star or planet. Weadopt the Boussinesq approximation and simulate Rayleigh-B\'enard convection,modelling the tidal flow as a background oscillatory shear flow. We demonstratethat the effective viscosity of both laminar and turbulent convection isapproximately frequency-independent for low frequencies. When the forcingfrequency exceeds the dominant convective frequency, the effective viscosityscales inversely with the square of the tidal frequency. We also show thatnegative effective viscosities are possible, particularly for high frequencytidal forcing, suggesting the surprising possibility of tidal anti-dissipation.These results are supported by a complementary high frequency asymptoticanalysis that extends prior work by Ogilvie & Lesur. We discuss theimplications of these results for interpreting the orbital decay of hotJupiters, and for several other astrophysical problems.

Tidal flows with convection: frequency-dependence of the effective viscosity and evidence for anti-dissipation